Hausdorff Measures

Classic book on measure theory with a foreword by the best name in the field.

C. A. Rogers (Author), Kenneth Falconer (Foreword by)

9780521624916, Cambridge University Press

Paperback, published 22 October 1998

228 pages
22.8 x 15.1 x 1.4 cm, 0.315 kg

'… well-known and beautiful book … written with notable clarity and precision …' European Mathematical Society

When it was first published this was the first general account of Hausdorff measures, a subject that has important applications in many fields of mathematics. There are three chapters: the first contains an introduction to measure theory, paying particular attention to the study of non-s-finite measures. The second develops the most general aspects of the theory of Hausdorff measures, and the third gives a general survey of applications of Hausdorff measures followed by detailed accounts of two special applications. This edition has a foreword by Kenneth Falconer outlining the developments in measure theory since this book first appeared. Based on lectures given by the author at University College London, this book is ideal for graduate mathematicians with no previous knowledge of the subject, but experts in the field will also want a copy for their shelves.

Foreword Kenneth Falconer
Preface
Part I. Measures in Abstract, Topological and Metric Spaces: 1. Introduction
2. Measures in abstract spaces
3. Measures in topological spaces
4. Measures in metric spaces
5. Lebesgue measure in n-dimensional Euclidean space
6. Metric measures in topological spaces
7. The Souslin operation
Part II. Hausdorff Measures: 8. Definition of Hausdorff measures and equivalent definitions
9. Mappings, special Hausdorff measures, surface areas
10. Existence theorems
11. Comparison theorems
12. Souslin sets
13. The increasing sets lemma and its consequences
14. The existence of comparable net measures and their properties
15. Sets of non-?-finite measure
Part III. Applications of Hausdorff Measures: 16. A survey of applications of Hausdorff measures
17. Sets of real numbers defined in terms of their expansions into continued fractions
18. The space of non-decreasing continuous functions defined on the closed unit interval
Bibliography
Appendix
Index.

Subject Areas: Real analysis, real variables [PBKB]